nbits = 8;      % 濾波器階數
maxbin = 2^nbits-1;     
n=3;             % 濾波器的階數為n-1
Wn = 0.2;       % 濾波器的截止頻率
Rp = 1.5;       % 通帶內波紋的分貝值
w = 128;        % 頻率點數目
% 連續切比雪夫濾波器設計 
[b1,a1]=cheby1(n-1,Rp, Wn); 
[h,w]=freqz(b1,a1,w);   % 頻率響應
h=abs(h);       % 幅頻響應
plot(w, h);
title ('Frequency response using non-integer variables')
x = [b1,a1];        % 設計變量

% 設置x的最大最小邊界值
if (any(x < 0))
    maxbin = floor (maxbin/2);
    vlb = -maxbin * ones(1, 2*n)-1;
    vub = maxbin * ones(1, 2*n); 
else
    vlb = zeros(1,2*n); 
    vub = maxbin * ones(1, 2*n); 
end

%歸一化濾波器系數
[m, mix] = max(abs(x)); 
factor =  maxbin/m; 
x =  factor * x;    % 
xorig = x;
xmask = 1:2*n;
xmask([mix]) = [];
nx = 2*n; 
% 設置算法終止準則，加速解的收斂
options = optimset('Display','iter','TolX',0.1,…
'TolFun',1e-3,'TolCon',1e-6);
if length(w) == 1
   options = optimset(options,'MinAbsMax',w);
else
   options = optimset(options,'MinAbsMax',length(w));
end
%離散化第一個變量
[x, xmask] = elimone(x, xmask, h, w, n, maxbin)

niters = length(xmask); 
for m = 1:niters
%計算最優的離散整數值
x(xmask) = fminimax('filtobj',x(xmask),[],[],[],[],vlb(xmask),…
vub(xmask),'filtcon',options, x, xmask, n, h, maxbin);
[x, xmask] = elimone(x, xmask, h, w, n, maxbin);
end

xold = x;
xmask = 1:2*n;
xmask([n+1, mix]) = [];
x = x + 0.5; 
for i = xmask
    [x, xmask] = elimone(x, xmask, h, w, n, maxbin);
end
xmask = 1:2*n;
xmask([n+1, mix]) = [];
x= x - 0.5;
for i = xmask
    [x, xmask] = elimone(x, xmask, h, w, n, maxbin);
end
if any(abs(x) > maxbin)
x = xold;
end

% 優化濾波器的頻率響應
subplot(211)
bo = x(1:n); 
ao = x(n+1:2*n); 
h2 = abs(freqz(bo,ao,128));
plot(w,h,w,h2,'o')
title('Optimized filter versus original')